Scalable backpropagation for Gaussian Processes using celerite

TL;DR

This paper introduces a scalable, memory-efficient backpropagation method for Gaussian Processes using the celerite algorithm, enabling faster gradient computations suitable for large datasets.

Contribution

It derives a novel backpropagation algorithm for celerite-based Gaussian Processes, improving efficiency and scalability over existing automatic differentiation methods.

Findings

Linear computational scaling with data size

Reduced memory usage compared to traditional methods

Compatible with automatic differentiation frameworks

Abstract

This research note presents a derivation and implementation of efficient and scalable gradient computations using the celerite algorithm for Gaussian Process (GP) modeling. The algorithms are derived in a "reverse accumulation" or "backpropagation" framework and they can be easily integrated into existing automatic differentiation frameworks to provide a scalable method for evaluating the gradients of the GP likelihood with respect to all input parameters. The algorithm derived in this note uses less memory and is more efficient than versions using automatic differentiation and the computational cost scales linearly with the number of data points.